484 LAPLACE. 



he retains the same vakies oip and q as before, and he obtains 



1 



P = 



328269 • 



It will be seen that the new values of p and q make - a little 



larger than the old values ; hence it is natural that P should be 

 increased. 



903. Laplace gives in the memoir some important investiga- 

 tions on the probability of future events as deduced from ob- 

 served events; these are reproduced in the Theorie . . . des Proh. 

 pages 394—396. 



904. Laplace devotes the last ten pages of his memoir to 

 the theory of errors ; he says that after his memoir in the sixth 

 volume of the Memoires...par divers Savans the subject had been 

 considered by Lagrange, Daniel Bernoulli and Euler. Since, how- 

 ever, their principles differed from his own he is induced to resume 

 the investigation, and to present his results in such a manner as to 

 leave no doubt of their exactness. Accordingly he gives, with 

 some extension, the same theory as before ; see Art. 874. The 

 theory does not seem, however, to have any great value. 



905. The present memoir deserves to be regarded as very im- 

 portant in the history of the subject. The method of approxima- 

 tion to the values of definite integrals, which is here expounded, 

 must be esteemed a great contribution to mathematics in general 

 and to our special department in particular. The applications 

 made to the problems respecting births shew the power of the 

 method and its peculiar value in the- theory of probability. 



906. Laplace's next memoir on our subject is entitled Memoir e 

 sur les Suites; it is published in the volume for 1779 of the 

 Histoire de l' A cad... Paris; the date of publication is 1782. The 

 memoir occupies pages 207 — 809 of the volume. 



This memoir contains the theory of Generating Functions. 

 With the exception of pages 269 — 286 the whole memoir is 

 reproduced almost identically in the T}ieorie..,des Proh.; it forms 

 pages 9 — 80 of the work. The pages which are not reproduced 



